function [theta2,x2]=ps5p2_stage2(tildez);
% this function computes the roots of the function ps5p2_stage2_zero,
% using the knowledge we have about the shape of that function
global ALPHAX ALPHAZ ALPHA BETA DELTA ALPHATILDEZ B C X1STAR SELECT OPTIONS...
THETA2LOWER THETA2UPPER THETA1STAR ZUNDERBAR ZUPPERBAR;
% we know that the function goes to minus infinity as theta2 goes to 0,
% so we can find theta2lower at which the function is negative
% we also know that the function goes to plus infinity as theta2 goes to1,
% so we can find theta2upper at which the function is positive
theta2lower=find_bound_converge('ps5p2_stage2_zero','right',-1,0.1,1,0,tildez);
theta2upper=find_bound_converge('ps5p2_stage2_zero','left',1,0.1,1,1,tildez);
if (tildez<=ZUNDERBAR)|(tildez>=ZUPPERBAR) % this is the case of uniquenesss
% if it to close to the boundaries, set theta2=1 or theta2=0 respectively,
% otherwise compute it using fzero
if isinf(ps5p2_stage2_zero(theta2upper,tildez))
theta2=1;
elseif isinf(ps5p2_stage2_zero(theta2lower,tildez))
theta2=0;
else
theta2=fzero('ps5p2_stage2_zero',[theta2lower theta2upper],OPTIONS,tildez);
end
% next check whether it is indeed an equilibrium, if not replace it
% with what is the equilibrium
theta2=max(theta2,THETA1STAR);
if theta2>THETA1STAR
x2=ps5p2_X(theta2);
else
theta2=THETA1STAR;
x2=ps5p2_Xbinding(theta2,tildez);
end
else % this is the case of potential multiplicity
[theta2max,maxvalue]=fmaxbndn('ps5p2_stage2_zero',theta2lower,0.5,1,OPTIONS,[],tildez);
[theta2min,minvalue]=fminbndn('ps5p2_stage2_zero',0.5,theta2upper,1,OPTIONS,[],tildez);
if isinf(ps5p2_stage2_zero(theta2lower,tildez))
theta2left=0;
else
theta2left=fzero('ps5p2_stage2_zero',[theta2lower theta2max],OPTIONS,tildez);
end
if isinf(ps5p2_stage2_zero(theta2upper,tildez))
theta2right=1;
else
theta2right=fzero('ps5p2_stage2_zero',[theta2min theta2upper],OPTIONS,tildez);
end
if SELECT==0 % this selects the lower equilibrium
if (theta2leftTHETA1STAR
theta2=theta2left;
x2=ps5p2_X(theta2);
else
theta2=THETA1STAR;
x2=ps5p2_Xbinding(theta2,tildez);
end
end
else % this selects the higher equilibrium
if theta2right>THETA1STAR
theta2=theta2right;
x2=ps5p2_X(theta2);
else
theta2=THETA1STAR;
x2=ps5p2_Xbinding(theta2,tildez);
end
end
end